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In this letter, we study the proximal gradient dynamics. This recently-proposed continuous-time dynamics solves optimization problems whose cost functions are separable into a nonsmooth convex and a smooth component. First, we show that the cost function decreases monotonically along the trajectories of the proximal gradient dynamics. We then introduce a new condition that guarantees exponential convergence of the cost function to its optimal value, and show that this condition implies the proximal Polyak-{\L}ojasiewicz condition. We also show that the proximal Polyak-{\L}ojasiewicz condition guarantees exponential convergence of the cost function. Moreover, we extend these results to time-varying optimization problems, providing bounds for equilibrium tracking. Finally, we discuss applications of these findings, including the LASSO problem, quadratic optimization with polytopic constraints, and certain matrix based problems., Comment: Submitted to IEEE L-CSS and ACC, 6 pages

We have modified the metal-assisted transfer technique to obtain large-area few-layer flakes from transition metal dichalcogenides bulk crystals by introducing an initial stage - exfoliation of the bulk crystal onto an intermediate substrate, specifically a silicon wafer coated with polyvinyl alcohol. Following this, we thermally evaporate silver onto the sample and transfer the top layers of the crystal along with the silver layer to the target substrate. This technique allows the production of visually non-corrugated single- and few-layer flakes with high yield. A direct comparison of the micro-Raman and micro-photoluminescence spectra of flakes exfoliated using our method with the spectra of those exfoliated from scotch tape reveals differences in their properties. We identify signatures of deformations in the flakes exfoliated from the intermediate substrate, indicating the presence of static friction between the substrate and the flake. Our findings thus suggest a novel method to induce intrinsic deformation in 2D materials., Comment: 6 pages 4 figures; Supplementary available on request

We suggest a method for simultaneously generating high order quadrature weights for integrals over Lipschitz domains and their boundaries that requires neither meshing nor moment computation. The weights are determined on pre-defined scattered nodes as a minimum norm solution of a sparse underdetermined linear system arising from a discretization of a suitable boundary value problem by either collocation or meshless finite differences. The method is easy to implement independently of the domain's representation, since it only requires as inputs the position of all quadrature nodes and the direction of outward-pointing normals at each node belonging to the boundary. Numerical experiments demonstrate the robustness and high accuracy of the method on a number of smooth and piecewise smooth domains in 2D and 3D, including some with reentrant corners and edges.

The present work is the continuation of our paper [1]. It is devoted to the modeling of the interplay of equilibrium and non-equilibrium phase transitions. The modeling of equilibrium phase transition is based on the modified Cahn-Hilliard equation. The non-equilibrium phase transition is modeled by the Second Schl\"ogl reaction system. We consider the advancing front, which combines these both transitions. Different from [1], we consider here the memory effects, i.e. the effects of non-Fickian diffusion. The traveling wave solution is obtained, its dependence on the model parameters is studied in detail. The relative importance of memory effects for different process regimes is estimated., Comment: arXiv admin note: text overlap with arXiv:2002.07597

We report a twisted triple bilayer graphene platform consisting of three units of Bernal bilayer graphene (BLG) consecutively twisted at 1.49{\deg} and 1.68{\deg}. We observe inter-moir\'e Hofstadter butterflies from two co-existing moir\'e superlattices and a Hofstadter butterfly from reconstructed moir\'e-of-moir\'e lattice, and show that their Brown-Zak (BZ) oscillations quantitatively agree with each other, both evidencing strong atomic reconstruction with a lattice constant of 18.1 nm. We further demonstrate such atomic reconstruction strongly enhances the Berry curvature of each moir\'e and moir\'e-of-moir\'e band-insulator state, characterized by measured strong non-local valley Hall effect (VHE) that sensitively depends on the inter-moir\'e competition strength, tunable by manipulating the out-of-the-plane carrier distribution which controls the magnitude of the valley currents. Our study sheds new light on the microscopic mechanism of atomic and electronic reconstruction in twisted-multilayer systems, by investigating novel emergent quantum phenomena of reconstructed quasi-crystalline moir\'e-of-moir\'e superlattice, including a new type of moir\'e-of-moir\'e band-insulator states and atomically enhanced moir\'e Berry curvature. We show that the reconstructed electronic band can be versatilely tuned by electrostatics, providing an approach towards engineering the band structure and its topology for a novel quantum material platform with designer electrical and optical properties.

Gravitational shockwaves are geometries where components of the transverse curvature have abrupt behaviour across null hypersurfaces, which are fronts of the waves. We develop a general approach to describe classical field theories on such geometries in a linearized approximation, by using free scalar fields as a model. Perturbations caused by shockwaves exist above the wave front and are solutions to a characteristic Cauchy problem with initial data on the wave front determined by a supertranslation of ingoing fields. A special attention is paid to perturbations of fields of pointlike sources generated by plane-fronted gravitational shockwaves. One has three effects: conversion of non-stationary perturbations into an outgoing radiation, a spherical scalar shockwave which appears when the gravitational wave hits the source, and a plane scalar shockwave accompanying the initial gravitational wave. Our analysis is applicable to gravitational shockwaves of a general class including geometries sourced by null particles and null branes., Comment: 29 pages, 4 figures

Broadband absorption in the visible spectrum is essential in optoelectronic applications that involve power conversion such as photovoltaics and photocatalysis. Most ultrathin broadband absorbers use parasitic plasmonic structures that maximize absorption using surface plasmons and/or Fabry-Perot cavities, which limits the weight efficiency of the device. Here, we show the theoretical and experimental realization of an unpatterned/planar semiconductor thin-film absorber based on monolayer transition metal dichalcogenides (TMDCs). We experimentally demonstrate an average total absorption in the visible range (450 nm - 700 nm) of > 70% using > 4 nm of semiconductor absorbing materials scalable over large areas with vapor phase growth techniques. Our analysis suggests that a power conversion efficiency (PCE) of 15.54% and a specific power > 300 W g^-1 may be achieved in a photovoltaic cell based on this metamaterial absorber.

Animal Re-ID is crucial for wildlife conservation, yet it faces unique challenges compared to person Re-ID. First, the scarcity and lack of diversity in datasets lead to background-biased models. Second, animal Re-ID depends on subtle, species-specific cues, further complicated by variations in pose, background, and lighting. This study addresses background biases by proposing a method to systematically remove backgrounds in both training and evaluation phases. And unlike prior works that depend on pose annotations, our approach utilizes an unsupervised technique for feature alignment across body parts and pose variations, enhancing practicality. Our method achieves superior results on three key animal Re-ID datasets: ATRW, YakReID-103, and ELPephants., Comment: Accepted to CVPR workshop CV4Animals 2024

The Super-Kamiokande and T2K collaborations present a joint measurement of neutrino oscillation parameters from their atmospheric and beam neutrino data. It uses a common interaction model for events overlapping in neutrino energy and correlated detector systematic uncertainties between the two datasets, which are found to be compatible. Using 3244.4 days of atmospheric data and a beam exposure of $19.7(16.3) \times 10^{20}$ protons on target in (anti)neutrino mode, the analysis finds a 1.9$\sigma$ exclusion of CP-conservation (defined as $J_{CP}=0$) and a preference for the normal mass ordering., Comment: 10 pages, 3 figures

Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction theory. These opinions are (i) contraction theory is a unifying framework emerging from classical and modern works, (ii) contractivity is computationally-friendly, robust, and modular stability, (iii) numerous dynamical systems are contracting, (iv) contraction theory is relevant to modern applications, and (v) contraction theory can be vastly extended in numerous directions. We survey recent theoretical and applied research in each of these five directions.

The valley degree of freedom in 2D materials can be manipulated for low-dissipation quantum electronics called valleytronics. At the boundary between two regions of bilayer graphene with different atomic or electrostatic configuration, valley-polarized current has been realized. However, the demanding fabrication and operation requirements limit device reproducibility and scalability toward more advanced valleytronics circuits. We demonstrate a new device architecture of a point junction where a valley-chiral 0D PN junction is easily configured, switchable, and capable of carrying valley current with an estimated polarization of ~80%. This work provides a new building block in manipulating valley quantum numbers and scalable valleytronics.

Even the best current algorithms for estimating body 3D shape and pose yield results that include body self-intersections. In this paper, we present CLOAF, which exploits the diffeomorphic nature of Ordinary Differential Equations to eliminate such self-intersections while still imposing body shape constraints. We show that, unlike earlier approaches to addressing this issue, ours completely eliminates the self-intersections without compromising the accuracy of the reconstructions. Being differentiable, CLOAF can be used to fine-tune pose and shape estimation baselines to improve their overall performance and eliminate self-intersections in their predictions. Furthermore, we demonstrate how our CLOAF strategy can be applied to practically any motion field induced by the user. CLOAF also makes it possible to edit motion to interact with the environment without worrying about potential collision or loss of body-shape prior., Comment: CVPR 2024, 13 pages

In this letter, we investigate sufficient conditions for the exponential stability of LTI systems driven by controllers derived from parametric optimization problems. Our primary focus is on parametric projection controllers, namely parametric programs whose objective function is the squared distance to a nominal controller. Leveraging the virtual system method of analysis and a novel contractivity result for Lur'e systems, we establish a sufficient LMI condition for the exponential stability of an LTI system with a parametric projection-based controller. Separately, we prove additional results for single-integrator systems. Finally, we apply our results to state-dependent saturated control systems and control barrier function-based control and provide numerical simulations.

We analyze the convergence behavior of \emph{globally weakly} and \emph{locally strongly contracting} dynamics. Such dynamics naturally arise in the context of convex optimization problems with a unique minimizer. We show that convergence to the equilibrium is \emph{linear-exponential}, in the sense that the distance between each solution and the equilibrium is upper bounded by a function that first decreases linearly and then exponentially. As we show, the linear-exponential dependency arises naturally in certain dynamics with saturations. Additionally, we provide a sufficient condition for local input-to-state stability. Finally, we illustrate our results on, and propose a conjecture for, continuous-time dynamical systems solving linear programs., Comment: 16 pages, 4 Figures

Imposing incommensurable periodicity on the periodic atomic lattice can lead to complex structural phases consisting of locally periodic structure bounded by topological defects. Twisted trilayer graphene (TTG) is an ideal material platform to study the interplay between different atomic periodicities, which can be tuned by twist angles between the layers, leading to moir\'e-of-moir\'e lattices. Interlayer and intralayer interactions between two interfaces in TTG transform this moir\'e-of-moir\'e lattice into an intricate network of domain structures at small twist angles, which can harbor exotic electronic behaviors. Here we report a complete structural phase diagram of TTG with atomic scale lattice reconstruction. Using transmission electron microscopy combined with a new interatomic potential simulation, we show that a cornucopia of large-scale moir\'e lattices, ranging from triangular, kagome, and a corner-shared hexagram-shaped domain pattern, are present. For small twist angles below 0.1{\deg}, all domains are bounded by a network of two-dimensional domain wall lattices. In particular, in the limit of small twist angles, the competition between interlayer stacking energy and the formation of discommensurate domain walls leads to unique spontaneous symmetry breaking structures with nematic orders, suggesting the pivotal role of long-range interactions across entire layers. The diverse tessellation of distinct domains, whose topological network can be tuned by the adjustment of the twist angles, establishes TTG as a platform for exploring the interplay between emerging quantum properties and controllable nontrivial lattices.

Global stability and robustness guarantees in learned dynamical systems are essential to ensure well-behavedness of the systems in the face of uncertainty. We present Extended Linearized Contracting Dynamics (ELCD), the first neural network-based dynamical system with global contractivity guarantees in arbitrary metrics. The key feature of ELCD is a parametrization of the extended linearization of the nonlinear vector field. In its most basic form, ELCD is guaranteed to be (i) globally exponentially stable, (ii) equilibrium contracting, and (iii) globally contracting with respect to some metric. To allow for contraction with respect to more general metrics in the data space, we train diffeomorphisms between the data space and a latent space and enforce contractivity in the latent space, which ensures global contractivity in the data space. We demonstrate the performance of ELCD on the high dimensional LASA, multi-link pendulum, and Rosenbrock datasets., Comment: 9 pages, 3 figures. Under Review

When enough annotated training data is available, supervised deep-learning algorithms excel at estimating human body pose and shape using a single camera. The effects of too little such data being available can be mitigated by using other information sources, such as databases of body shapes, to learn priors. Unfortunately, such sources are not always available either. We show that, in such cases, easy-to-obtain unannotated videos can be used instead to provide the required supervisory signals. Given a trained model using too little annotated data, we compute poses in consecutive frames along with the optical flow between them. We then enforce consistency between the image optical flow and the one that can be inferred from the change in pose from one frame to the next. This provides enough additional supervision to effectively refine the network weights and to perform on par with methods trained using far more annotated data., Comment: 21 pages; TMLR

The Mu2e experiment at Fermilab searches for the neutrino-less conversion of a negative muon into an electron, with a distinctive signature of a mono-energetic electron with energy of 104.967 MeV. The calorimeter is made of two disks of pure CsI crystals, each read out by two custom large area UV-extended SiPMs. It plays a fundamental role in providing excellent particle identification capabilities and an online trigger filter while improving the track reconstruction, requiring better than 10% energy and 500 ps timing resolutions for 100 MeV electrons. In this paper, we present the status of construction and the Quality Control (QC) performed on the produced crystals and photosensors, the development of the rad-hard electronics, and the most important results of the irradiation tests. Construction of the mechanics is also reported. Status and plans for the calorimeter assembly and its first commissioning are described.

A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing that this method has a significantly higher convergence rate and accuracy than the vanilla physics-informed neural networks (PINN) and even SPINN based on a system of partial differential equations (PDEs). In addition, using the SPINN in the framework of DEM approach it is possible to solve problems of the linear theory of elasticity on complex geometries, which is unachievable with the help of PINNs in frames of partial differential equations. Considered problems are very close to the industrial problems in terms of geometry, loading, and material parameters.

In the literature, lines of the projective space $\mathrm{PG}(3,q)$ are partitioned into classes, each of which is a union of line orbits under the stabilizer group of the twisted cubic. The least studied class is named $\mathcal{O}_6$. This class contains lines external to the twisted cubic which are not its chords or axes and do not lie in any of its osculating planes. For even and odd $q$, we propose a new family of orbits of $\mathcal{O}_6$ and investigate in detail their stabilizer groups and the corresponding submatrices of the point-line and plane-line incidence matrices. To obtain these submatrices, we explored the number of solutions of cubic and quartic equations connected with intersections of lines (including the tangents to the twisted cubic), points, and planes in $\mathrm{PG}(3,q)$., Comment: 28 pages. arXiv admin note: text overlap with arXiv:2209.04910, arXiv:2210.12821

Dark matter may consist of axion-like particles (ALPs). When polarized electromagnetic radiation passes through the dark-matter media, interaction with background ALPs affects the polarization of photons. The condensate of axionic dark matter experiences periodic oscillations, and the period of the oscillations is of order of years for ultra-light dark matter. This would result in observable periodic changes in the polarization plane, determined by the phases of the ALP field at the Earth and at the source. In this paper, we use recent polarimetric observations of the HL Tauri protoplanetary disk performed in different years to demonstrate the lack of changes of polarization angles, and hence to constrain masses and photon couplings of the hypothetical axion-like ultralight dark matter., Comment: 4 pages, 2 figures, results in sec. III were corrected. Submitted to Phys. Rev. D

The critical behaviour of laser-induced changes in magnetic ordering is studied experimentally in two-dimensional zigzag antiferromagnets $XY$-like NiPS$_3$ and Ising-like FePS$_3$. To examine laser-induced dynamics in flakes of these compounds, we employ time-resolved exchange linear dichroism effect sensitive to zigzag magnetic ordering and independent of the orientation of the antiferromagnetic vector. In both compounds laser excitation in the vicinity of the absorption edge induces partial quenching of the antiferromagnetic ordering manifested by exchange linear dichroism reduction. The amplitude of the effect varies with temperature as the derivative of the antiferromagnetic vector and exhibits a critical behaviour with the exponents corresponding to $XY$- and Ising-models for NiPS$_3$ and FePS$_3$, respectively. Critical slowing down of the demagnetization in the vicinity of N\'eel temperature is found, however, only in FePS$_3$. In contrast, the increase of the demagnetization time near the ordering temperature in NiPS$_3$ is minor. We show that the difference in the demagnetization times correlates well with the spin specific heat in both compounds. Beyond the range of slowing down, the demagnetization times in NiPS$_3$ and FePS$_3$ are comparable, about 5 - 10 ps, and are longer than those reported earlier for CoPS$_3$ and considerably shorter than for MnPS$_3$. This points to the importance of the unquenched angular momentum of transition-metal ions in laser-induced demagnetization process., Comment: 12 pages, 6 figures

We fabricate a twisted trilayer graphene device with consecutive twist angles of 1.33 and 1.64 degrees, in which we electrostatically tune the electronic states from each of the two co-existing moir\'e superlattices and the interactions between them. When both moir\'e superlattices contribute equally to electrical transport, we report a new type of inter-moir\'e Hofstadter butterfly. Its Brown-Zak oscillation corresponds to one of the intermediate quasicrystal length scales of the reconstructed moir\'e of moir\'e (MoM) superlattice, shedding new light on emergent physics from competing atomic orders.

The vast high entropy alloy (HEA) composition space is promising for discovery of new material phases with unique properties. We explore the potential to achieve rare-earth-free high magnetic anisotropy materials in single-phase HEA thin films. Thin films of FeCoNiMnCu sputtered on thermally oxidized Si/SiO$_{2}$ substrates at room temperature are magnetically soft, with a coercivity on the order of 10 Oe. After post-deposition rapid thermal annealing (RTA), the films exhibit a single face-centered-cubic phase, with an almost 40-fold increase in coercivity. Inclusion of 50 at.% Pt in the film leads to ordering of a single L1$_{0}$ high entropy intermetallic phase after RTA, along with high magnetic anisotropy and 3 orders of magnitude coercivity increase. These results demonstrate a promising HEA approach to achieve high magnetic anisotropy materials using RTA., Comment: 28 pages, including 4 figures and 6 pages of supporting information (5 SI figures and 2 SI tables)

We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples

We propose and analyze a continuous-time firing-rate neural network, the positive firing-rate competitive network (\pfcn), to tackle sparse reconstruction problems with non-negativity constraints. These problems, which involve approximating a given input stimulus from a dictionary using a set of sparse (active) neurons, play a key role in a wide range of domains, including for example neuroscience, signal processing, and machine learning. First, by leveraging the theory of proximal operators, we relate the equilibria of a family of continuous-time firing-rate neural networks to the optimal solutions of sparse reconstruction problems. Then, we prove that the \pfcn is a positive system and give rigorous conditions for the convergence to the equilibrium. Specifically, we show that the convergence: (i) only depends on a property of the dictionary; (ii) is linear-exponential, in the sense that initially the convergence rate is at worst linear and then, after a transient, it becomes exponential. We also prove a number of technical results to assess the contractivity properties of the neural dynamics of interest. Our analysis leverages contraction theory to characterize the behavior of a family of firing-rate competitive networks for sparse reconstruction with and without non-negativity constraints. Finally, we validate the effectiveness of our approach via a numerical example., Comment: 26 pages, 9 Figure, 1 Table

We report the results of polarization-dependent Raman spectroscopy of phonon states in single-crystalline quasi-one-dimensional NbTe$_4$ and TaTe$_4$ van der Waals materials. The measurements were conducted in the wide temperature range from 80 K to 560 K. Our results show that although both materials have identical crystal structures and symmetries, there is a drastic difference in the intensity of their Raman spectra. While TaTe4 exhibits well-defined peaks through the examined frequency and temperature ranges, NbTe4 reveals extremely weak Raman signatures. The measured spectral positions of the phonon peaks agree with the phonon band structure calculated using the density-functional theory. We offer possible reasons for the in-tensity differences between the two van der Waals materials. Our results provide insights into the phonon properties of NbTe$_4$ and TaTe$_4$ van der Waals materials and indicate the potential of Raman spectroscopy for studying charge-density-wave quantum condensate phases., Comment: 24 pages; 6 figures; 1 table

Null cosmic strings are shown to disturb gravitational fields of massive bodies and create outgoing gravitational waves (GW). Perturbations of the metric caused by a straight null string and a point-like massive source are found as solutions to linearized Einstein equations on a flat space-time. An analytic approximation for their asymptotic at future null infinity is derived. A space-time created by the source and the string is shown to have asymptotically polyhomogeneous form. We calculate GW flux in such space-times and demonstrate that the averaged intensity of the radiation is maximal in the direction of the string motion. Opportunities to detect null string generated gravity waves are briefly discussed., Comment: 30 paqes, 2 figures, v2, where a new section, comments and references are added

The length function $\ell_q(r,R)$ is the smallest possible length $n$ of a $ q $-ary linear $[n,n-r]_qR$ code with codimension (redundancy) $r$ and covering radius $R$. Let $s_q(N,\rho)$ be the smallest size of a $\rho$-saturating set in the projective space $\mathrm{PG}(N,q)$. There is a one-to-one correspondence between $[n,n-r]_qR$ codes and $(R-1)$-saturating $n$-sets in $\mathrm{PG}(r-1,q)$ that implies $\ell_q(r,R)=s_q(r-1,R-1)$. In this work, for $R\ge3$, new asymptotic upper bounds on $\ell_q(tR+1,R)$ are obtained in the following form: $\hspace{0.7cm} \bullet~\ell_q(tR+1,R) =s_q(tR,R-1)\le \sqrt[R]{\frac{R!}{R^{R-2}}}\cdot q^{(r-R)/R}\cdot\sqrt[R]{\ln q}+o(q^{(r-R)/R}), \hspace{0.3cm}r=tR+1,~t\ge1,~ q\text{ is an arbitrary prime power},~q\text{ is large enough};$ $\hspace{0.7cm} \bullet~\text{ if additionally }R\text{ is large enough, then }\sqrt[R]{\frac{R!}{R^{R-2}}}\thicksim\frac{1}{e}\thickapprox0.3679. $ The new bounds are essentially better than the known ones. For $t=1$, a new construction of $(R-1)$-saturating sets in the projective space $\mathrm{PG}(R,q)$, providing sets of small sizes, is proposed. The $[n,n-(R+1)]_qR$ codes, obtained by the construction, have minimum distance $R + 1$, i.e. they are almost MDS (AMDS) codes. These codes are taken as the starting ones in the lift-constructions (so-called "$q^m$-concatenating constructions") for covering codes to obtain infinite families of codes with growing codimension $r=tR+1$, $t\ge1$., Comment: 24 pages. arXiv admin note: text overlap with arXiv:2108.13609

The ability to emit narrow exciton lines, preferably with a clearly defined polarization, is one of the key conditions for the use of nanostructures based on III-VI monochalcogenides and other layered crystals in quantum technology to create non-classical light. Currently, the main method of their formation is exfoliation followed by strain and defect engineering. A factor limiting the use of epitaxy is the presence of different phases in the grown films. In this work, we show that control over their formation makes it possible to create structures with the desired properties. We propose Ga$_2$Se$_3$/GaSe nanostructures by van der Waals epitaxy with a high VI/III flux ratio as a source of narrow exciton lines. Actually, these nanostructures are a combination of allotropes: GaSe and Ga$_2$Se$_3$, consisting of the same atoms in different arrangements. The energy position of the narrow lines is determined by the quantum confinement in Ga$_2$Se$_3$ inclusions of different sizes in the GaSe matrix, similar to quantum dots, and their linear polarization is due to the ordering of Ga vacancies in a certain crystalline direction in Ga$_2$Se$_3$. Such nanostructures exhibit single-photon emission with second-order correlation function $g^{(2)}(0)\sim$0.1 at 10 K that makes them promising for quantum technologies.